Problem: $B$ is the midpoint of $\overline{AC}$ $A$ $B$ $C$ If: $ AB = 9x + 6$ and $ BC = 5x + 22$ Find $AC$.
Solution: A midpoint divides a segment into two segments with equal lengths. ${AB} = {BC}$ Substitute in the expressions that were given for each length: $ {9x + 6} = {5x + 22}$ Solve for $x$ $ 4x = 16$ $ x = 4$ Substitute $4$ for $x$ in the expressions that were given for $AB$ and $BC$ $ AB = 9({4}) + 6$ $ BC = 5({4}) + 22$ $ AB = 36 + 6$ $ BC = 20 + 22$ $ AB = 42$ $ BC = 42$ To find the length $AC$ , add the lengths ${AB}$ and ${BC}$ $ AC = {AB} + {BC}$ $ AC = {42} + {42}$ $ AC = 84$